Electromagnetic shielding of superconducting quantum circuits
The article provides an overview of the shielding systems of quantum circuits used in leading scientific groups. The general requirements for the construction of such systems are outlined and the problems associated with a wide variety of materials and the absence of the methodology for their development are identified.
The superconductor quantum circuits  present one of the most promising trends in quantum computing. Nowadays, quantum superiority has already been achieved with the use of superconducting quantum structures – a quantum processor can solve a problem faster than the most powerful modern supercomputer . Many conditions are required for correct and error-free operation of quantum circuits: reduction of the induced charge , minimization of the external magnetic field fluctuations , ensuring current and voltage constancy of control and readout pulses  and protection against infrared (IR) radiation [5–8]. All these factors contribute to the destruction of the quantum system state, the so called decoherence process .
A special place in the decoherence process is occupied by IR radiation hitting the sample with the quantum circuit: the intrinsic power from IR photons hitting the chip is higher than a power from cosmic rays or background radiation . The incident radiation destroys Cooper pairs to form quasiparticles, which, when tunneling through the Josephson transition, cause both energy relaxation and dephasing of the qubit .
Fluctuations of the external magnetic field and the induced charge cause uncontrollable changes in the parameters included in the energy description of the quantum system – the Hamiltonian: in the Josephson energy EJ and the superconducting phase difference δ , as well as in the qubit frequency ω01. This leads to unpredictable changes of the qubit state.
Operation of superconductor qubits is only possible at a temperature significantly lower than the critical superconductor temperature (for aluminium Тс = 1.18 K). Qubits cooling to temperatures of 10 mK is realised with a special equipment – dissolution cryostat . To reduce the influence of IR radiation and other electromagnetic influences on the quantum circuit in the cryostat, shielding and filtering of coaxial signal lines are used in addition to the cryostat covers .
Shielding presents a system of nested screens surrounding a sample holder with a quantum processor. Shielding systems used by leading research groups in the field of quantum computing vary both in design and in the materials used. This paper provides an analysis of shielding requirements for protection against IR radiation and electromagnetic fields and an overview of shielding systems (designs and materials) for selecting screens for superconducting quantum circuits.
PRINCIPLES OF SHIELDING
Protection against IR radiation
The sources of IR radiation in the cryostat are :
- signal coaxial microwave lines transferring heat from the upper stages to the microwave lines;
- warmer cryostat stages;
- passive elements of the measuring circuit that dissipate electrical energy.
To protect against IR photons sources, the screens, and in some cases also the sample holder lid, are internally coated with special IR absorbing coatings [5–8, 12–14], whose absorption degree can reach 0.95 in the terahertz range of electromagnetic radiation. Commercially available resins [5–8, 12–15] (e.g. Stycast 2850 FT, Marconi LAO, Eccosorb CR-series, etc.) alone or in combination with additional particles on their surface (e.g. SiC powder of different particle sizes, carbon or graphite dust) are used as absorption coatings.
Protection against electric and magnetic fields
Sources of electromagnetic radiation include both natural sources and surrounding equipment . In general, shielding includes not only construction details in the form of enclosures but also electrical components such as filters . Enclosures prevent the propagation of interference energy in space, while filters prevent the propagation of interference through wires. The best shielding effect is achieved by using these components together [18, 19]. It is important to insert the filter at the inlet to the shield, but not inside it .
The principle of shielding from an electric field is to transfer the charge from the open space to the shield and to divert it into the ground . Therefore, for effective protection against the electric field, the screen must be made of a highly conductive material (copper, aluminium) with a good ground connection – the contact resistance with the ground must be as low as possible.
The shields made of ferromagnetic materials (permalloys (µ-metal, soft magnetic alloy) or steels) with high relative magnetic permeability μr are used against constant and slowly changing (up to 1 kHz) magnetic fields. In such a shield, the magnetic induction lines run mainly along its walls, which have a low magnetic resistance compared to the air space. The shielding quality here is mainly determined by the magnetic permeability of the screen [17, 20].
The operating principle of screens against an alternating high-frequency magnetic field is that an alternating EMF is excited in the screen, which creates alternating induction eddy currents (Foucault currents) . The magnetic field of these currents will be closed: inside the screen they will be directed towards the excitation field, and outside the screen they will be directed along it. The resulting field is attenuated inside the screen and amplified outside it, i.e., the field is displaced from the screen. This shielding is already dependent on the depth of field penetration at different frequencies ("skin effect") and starts to work well from frequencies above 1kHz. Non-magnetic and ferromagnetic materials are used for the shields which are chosen based on the depth of field penetration . Among the possible ones are: copper, aluminium, µ-metal, steel, zinc, etc.
Superconductors ensure good protection against the alternating electromagnetic fields, in an ideal conductor there are no alternating electric and magnetic fields: currents flow over the surface without penetrating deep into the metal . If there are no holes or gaps in the screen, there are no HF magnetic and electric fields either inside or outside the screen.
EXISTING SHIELDING SYSTEMS FOR QUANTUM CIRCUITS
Described below are the superconductor quantum circuit shielding systems used by leading scientific groups in their measurement circuits.
Princeton University (USA)
In the shielding schemes here copper is most commonly used as the sample holder material with the quantum circuit [12, 23] (Fig.1). In front of the holder an Eccosorb CR-110 based filter is placed in combination with an LPF (Low Pass Filter) standing outside the screens [12, 23, 24]. Behind the holder there is a screen with an absorption coating either based on Eccosorb CR-124 [23, 24] or using Stycast resin with SiC particles [12, 23]. The base of the shield is copper  or aluminium [23, 24], which is also superconductive. A µ-metal screen [12, 23, 24] is then used in the shielding, in some cases a double screen . Also, in some circuits Mylar (aluminised lavsan) is used in various places as an additional reflective layer [23, 24].
MIT Lincoln Lab (США), ETH Zurich (Switzerland)
The approach to shielding in these two groups is similar (Fig.1). The data on holder materials are rare, but based on work  it can be assumed that copper is preferred. Then, shields are installed, either of a single Cryoperm-10 (permalloy) [11, 26] or Cryoperm-10 with an aluminium cylinder inside [25, 27]. For specific protection against cosmic rays, a shielding of lead bars can be applied . Here too filters are also used: based on Eccosorb CR-110 [27, 28] or Eccosorb CR-124 , as well as LPF [26, 29] alone or combined with HPF (High Pass Filter) .
University of California (UC) Berkeley (USA)
Copper – uncoated  or gold-plated  as well as aluminium  are used to manufacture the holder (Fig.2). Then, either simple Cryoperm shielding  or staggered shielding is used: copper with absorption material [30, 32, 34], aluminium cylinder  or foil , Cryoperm [30, 32, 34]. The inlet line filtration is provided by commercially available LPF [34–36] and HPF  filters or self-made ones based on Eccosorb resin  or copper powder .
Delft University of Technology (The Netherlands)
The data on the holder is scarce but a copper holder occurs when an absorptive coating is applied on the inside of the holder  (Fig.2). Then a multi-layer shielding is applied: an aluminium shield and two shields made of Cryophy (a kind of magnetically soft alloy) . Eccosorb filters [37–39], located outside the screens, are used for filtering.
Most often no data are given for the holder material, however,  indicates that the holder is made of aluminium (Fig.3). The shielding is made as cylinder of Ammuneal cryoperm (a kind of magnetically soft alloy) with a coating of Eccosorb CR-124 inside [41, 42]. Also, in , based on Eccosorb CR-124 resin, the outer shell of the holder was made; here the µ-metal shielding was applied to all stages of the cryostat. Eccosorb filters are often used [41, 42].
Google AI Quantum (USA)
The holders are mainly made of aluminium [43, 44], in some cases the holder lid is covered with an absorbing material based on Stycast resin with SiC particles  (Fig.3). Then a µ-metal shield is installed [43, 44]. There is also a shielding design of in the form of an individual screen  over a sample with a quantum circuit, and an absorbing coating is also applied to the inside of such a screen. Line filtering takes place via industrial LPFs and LPFs for the infrared range [43–45].
Chalmers University of Technology (Sweden)
The holders are made of copper  or aluminium  (Fig.3). The shielding is multistage and applies to both the holder and the entire bottom plate of the cryostat . THE HOLDER SURROUNDS A COPPER SHIELD WITH AN ABSORPTION COATING, followed by a Cryoperm shield. The entire lower stage of the cryostat is surrounded by an absorption coated copper casing followed by a superconducting shield. The signal is filtered using a BPF (Band Pass Filter) and an Eccosorb filter.
Karlsruhe Institute of Technology (KIT) (Germany)
The holder is made either of copper  or of aluminium  (Fig.3). Cryoperm [48, 49] is used as shielding, to which a lead shield may be added internally in some cases . Sometimes, an industrial BPF filter is used .
Yale University (USA)
Aluminium  or copper  is used for the holders (Fig.4). The shielding is multi-stage: a copper shield with an absorption coating with carbon dust ("Carbon black"), then a cylinder of Alumetal (a kind of magnetically soft alloy) . Both LPF and Eccosorb filters are fitted .
No data is given for the holder materials. Shielding is either single made of Cryoperm  or staggered: Stycast coated copper with carbon dust and magnetically soft Ammuneal  (Fig.4). Filtration is done by means of LPF and Eccosorb filters [52, 53], in some cases  with Eccosorb being placed inside the screens.
Université Pierre et Marie Curie (France), Royal Holloway University of London (Great Britain), University of Maryland (USA)
The holders are made either of gilded copper  or of aluminium  (Fig.4). These groups share dual µ-metal shielding, but in different configurations: around the holder , around the whole cryostat , a combined version (holders and the lower stage of the cryostat) . Royal Holloway additionally installs a superconducting lead cylinder . The filtration approach varies: BPF at Université Pierre et Marie Curie , HPF at Royal Holloway  and LPF at the University of Maryland .
Analysis of shielding of quantum circuits performed by the leading scientific groups in the field of quantum computing shows that the requirements to shielding materials for electromagnetic shielding are fulfilled. The analysed shielding systems allow of revealing some regularities in shielding:
- multi-stage shielding;
- use of special radiation absorbing coatings based on Eccosorb or Stycast epoxy resins with the addition of SiC or carbon dust particles;
- use of superconducting shields or shields made of metals with high relative magnetic permeability.
However, with a variety of solutions for protecting quantum circuits from IR radiation and other electromagnetic interference, it is not entirely clear what the configuration and sequence of shielding should be, how many shields are required and where the absorption coating should be placed. Thus, among the problems in the shielding issue are:
- lack of criteria for assessing the effectiveness of shielding systems;
- ambiguity in the set of materials used in the shields;
- lack of a clear idea of how well the shielding performs the task of protecting the quantum circuit from external influences.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.